Sum of first n natural numbers in C Program

In C programming, finding the sum of the first n natural numbers is a common problem that can be solved using different approaches. The sum of first n natural numbers means adding all positive integers from 1 to n (i.e., 1 + 2 + 3 + ... + n).

For example, if n = 5, then the sum would be: 1 + 2 + 3 + 4 + 5 = 15

Syntax

sum = n * (n + 1) / 2

We have two main methods to calculate this sum −

• Method 1 − Using iterative approach with loops
• Method 2 − Using mathematical formula (more efficient)

Method 1 − Using Iterative Approach

In this method, we use a loop to iterate from 1 to n and add each number to get the total sum −

#include <stdio.h>

int main() {
    int n = 10;
    int sum = 0;
    
    for(int i = 1; i <= n; i++) {
        sum += i;
    }
    
    printf("Sum of first %d natural numbers: %d<br>", n, sum);
    return 0;
}

Sum of first 10 natural numbers: 55

Method 2 − Using Mathematical Formula

The mathematical formula for the sum of first n natural numbers is: sum = n * (n + 1) / 2. This approach is more efficient as it calculates the result in constant time −

#include <stdio.h>

int main() {
    int n = 10;
    int sum = n * (n + 1) / 2;
    
    printf("Sum of first %d natural numbers: %d<br>", n, sum);
    return 0;
}

Sum of first 10 natural numbers: 55

Comparison

Conclusion

The mathematical formula approach is preferred for calculating the sum of first n natural numbers as it provides constant time complexity. For large values of n, this method significantly outperforms the iterative approach.